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Motivated by applications in local stereology, a new rotational Croftonformula is derived for Minkowski tensors. For sets of positive reach, theformula shows how rotational averages of intrinsically defined Minkowskitensors on sections passing through the origin are related to the geometry ofthe sectioned set. In particular, for Minkowski tensors of order j-1 onj-dimensional linear subspaces, we derive an explicit formula for therotational average involving hypergeometric functions. Sectioning with linesand hyperplanes through the origin is considered in detail. We also study thecase where the sections are not restricted to pass through the origin. For setsof positive reach, we here obtain a Crofton formula for the integral mean ofintrinsically defined Minkowski tensors on j-dimensional affine subspaces.

Rotational Crofton formulae for Minkowski tensors and some affine counterparts